Basic Squaring / Square Roots

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SAT Math › Basic Squaring / Square Roots

Questions 1 - 10

Simplify:

$-\sqrt{6}(\sqrt{5}-\sqrt{2})$

$2\sqrt{3}-\sqrt{30}$

$2\sqrt{3}+\sqrt{30}$

$3\sqrt{2}-\sqrt{30}$

$12-\sqrt{30}$

$-\sqrt{30}-2\sqrt{3}$

Explanation

To simplify the problem, just distribute the radical to each term in the parentheses.

$\-\sqrt{6}(\sqrt{5}-\sqrt{2})\=-\sqrt{30}+\sqrt{12}\=-\sqrt{30}+2\sqrt{3}$

Simplify:

$-\sqrt{6}(\sqrt{5}-\sqrt{2})$

$2\sqrt{3}-\sqrt{30}$

$2\sqrt{3}+\sqrt{30}$

$3\sqrt{2}-\sqrt{30}$

$12-\sqrt{30}$

$-\sqrt{30}-2\sqrt{3}$

Explanation

To simplify the problem, just distribute the radical to each term in the parentheses.

$\-\sqrt{6}(\sqrt{5}-\sqrt{2})\=-\sqrt{30}+\sqrt{12}\=-\sqrt{30}+2\sqrt{3}$

Simplify:

$-\sqrt{6}(\sqrt{5}-\sqrt{2})$

$2\sqrt{3}-\sqrt{30}$

$2\sqrt{3}+\sqrt{30}$

$3\sqrt{2}-\sqrt{30}$

$12-\sqrt{30}$

$-\sqrt{30}-2\sqrt{3}$

Explanation

To simplify the problem, just distribute the radical to each term in the parentheses.

$\-\sqrt{6}(\sqrt{5}-\sqrt{2})\=-\sqrt{30}+\sqrt{12}\=-\sqrt{30}+2\sqrt{3}$

Simplfy the following radical $\sqrt{20x^{2}}$ .

$2x\sqrt{5}$

$2x\sqrt{10}$

$4\sqrt{5x}$

$2\sqrt{5x^{2}}$

Explanation

You can rewrite the equation as $\sqrt{20x^2}=(x)\sqrt{5} \cdot \sqrt{4}$ .

This simplifies to $2x\sqrt{5}$ .

Simplfy the following radical $\sqrt{20x^{2}}$ .

$2x\sqrt{5}$

$2x\sqrt{10}$

$4\sqrt{5x}$

$2\sqrt{5x^{2}}$

Explanation

You can rewrite the equation as $\sqrt{20x^2}=(x)\sqrt{5} \cdot \sqrt{4}$ .

This simplifies to $2x\sqrt{5}$ .

Evaluate and simplify:

$\sqrt{10}*\sqrt{12}$

$2\sqrt{30}$

$\sqrt{22}$

$4\sqrt{5}$

$20\sqrt{6}$

$30\sqrt{2}$

Explanation

To multiply square roots, we multiply the numbers inside the radical and we can simplify them if possible.

$\ \sqrt{10}*\sqrt{12}\=\sqrt{10*12}\=\sqrt{120}\=\sqrt{4}*\sqrt{30}\=2\sqrt{30}$

Simplfy the following radical $\sqrt{20x^{2}}$ .

$2x\sqrt{5}$

$2x\sqrt{10}$

$4\sqrt{5x}$

$2\sqrt{5x^{2}}$

Explanation

You can rewrite the equation as $\sqrt{20x^2}=(x)\sqrt{5} \cdot \sqrt{4}$ .

This simplifies to $2x\sqrt{5}$ .

Evaluate and simplify:

$\sqrt{10}*\sqrt{12}$

$2\sqrt{30}$

$\sqrt{22}$

$4\sqrt{5}$

$20\sqrt{6}$

$30\sqrt{2}$

Explanation

To multiply square roots, we multiply the numbers inside the radical and we can simplify them if possible.

$\ \sqrt{10}*\sqrt{12}\=\sqrt{10*12}\=\sqrt{120}\=\sqrt{4}*\sqrt{30}\=2\sqrt{30}$

Evaluate and simplify:

$\sqrt{10}*\sqrt{12}$

$2\sqrt{30}$

$\sqrt{22}$

$4\sqrt{5}$

$20\sqrt{6}$

$30\sqrt{2}$

Explanation

To multiply square roots, we multiply the numbers inside the radical and we can simplify them if possible.

$\ \sqrt{10}*\sqrt{12}\=\sqrt{10*12}\=\sqrt{120}\=\sqrt{4}*\sqrt{30}\=2\sqrt{30}$

Simplify: $\sqrt{7}*\sqrt{14}$

$7\sqrt{2}$

$\sqrt{98}$

$\sqrt{21}$

$7\sqrt{3}$

$2\sqrt{7}$

Explanation

When multiplying square roots, you are allowed to multiply the numbers inside the square root. Then simplify if necessary.

$\sqrt{7}*\sqrt{14}=\sqrt{7*14}=\sqrt{98}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$

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